Heat a dutch oven over medium high heat. Add oil and continue to heat till it starts to smoke. Dry chicken thighs. Season with salt and pepper. Add chicken to dutch oven. Cook till chicken is crisp and brown.
While first side of chicken cooks prepare veggies (You can add a couple cloves of garlic if you like.)
When chicken is well browned and crisp, turn.
When 2nd side is well browned, remove to a plate and drain most of the fat from the pan leaving the fond.
Add veggies to pan and saute.
Continue to cook veggies till well caramelized. Be careful to not burn.
Deglaze pan with sherry.
Add chicken stock, wings, and thighs. Bring to a simmer and cook till very tender (about 45 minutes).
While chicken cooks, make the batter for the dumplings. You want to pour the melted, but cooled butter into the cold buttermilk.
Stir the butter into the buttermilk in a small bowl. Idea here is that the butter should congeal into little globules. In another, larger bowl, combine the flour, baking soda, sugar, and salt.
Remove the chicken from the stock and allow to cool. When chicken is cool enough to handle, pull it off the bones, discarding the skin and bones.
The stock will be rather fatty. Allow to sit a bit, and then remove as much fat as you can.
Add the parsley to the stock and adjust the seasoning. Using a whisk, whip the egg white into the buttermilk mixture. Using a spatula, turn the buttermilk mixture into the flour mixture. You want to just bring it all together and not work it too much. Add extra buttermilk if necessary.
Add the chicken meat back into the stock and return stock to a simmer. Drop dumplings into the simmering stock.
Wrap the top of the dutch oven in a towel. This is to stop condensation from dropping back onto the dumplings.
Cover the dutch oven and simmer gently till dumplings are done (about 15 minutes)
Dumplings should swell to about double their size.
Plate and serve :)